Committing to a collegiate career with Boston University for 2008, Cohen began the 2006–07 season with the USNTDP before leaving, citing unhappiness within his role, to join the Lincoln Stars of the United States Hockey League.[3][4] In his lone season with the Stars, Cohen established his offensive prowess and led the entire USHL among defensemen with 60 points in 53 games to earn a place in the USHL Second All-Star Team.[5]

In his sophomore year, Colby enjoyed his most successful collegiate season as BU advanced to the Frozen Four Tournament.[7] In 43 games he compiled 8 Goals and 24 Assists to finish second among Terrier defensemen with 32 Points, while also posting a Plus/Minus of 24 to finish fifth overall in the country.[7] Colby earned selection to the Frozen Four All-Tournament Team and was named the Most Outstanding Player of the Tournament after scoring the overtime game-winning Goal, from a pass from Defense partner Shattenkirk, in a 4–3 victory over the Miami Redhawks to win the 2009 National Championship.[7][8][9][7]

Returning for his junior campaign with the Terriers in 2009–10, Cohen was named as Player of the Month in January but was unable to help the team defend its National Championship after losing in the Hockey East Semi-finals.[10][11] Cohen was named to the Hockey East First All-Star Team and the NCAA East First All-American Team as he led the team's defense with 30 points in 36 games, scoring 14 Goals which were the most scored in a single season by a BU Defenseman in over 30 years.[12][2] Following elimination, Cohen brought an end to his collegiate career, signing an entry level contract alongside Shattenkirk, with the Avalanche on April 3, 2010.[6]

Upon signing with the Avalanche, he moved directly into the AHL and made his professional debut with the Lake Erie Monsters.[6] He finished the 2009–10 season with one assist in three games.[2]

Prior to the 2010–11 season, Cohen attended his first Avalanche training camp and was among the final cuts assigned to Lake Erie on October 3, 2010.[13] After starting the season with the Monsters, Cohen was recalled by the injury-depleted Avalanche and made his NHL debut in a 5–0 shutout win against the Dallas Stars on November 6, 2010.[14][15] In his ascension to the NHL, Cohen again joined Shattenkirk as a teammate along the blueline.[16]

After three games with the Avalanche, Cohen was returned to Lake Erie before being traded to the Boston Bruins for Matt Hunwick on November 29, 2010.[17][14] On April 14, 2011, Cohen was called up by the Boston Bruins as a spare for the playoffs, but he did not play so his name was not engraved on the Stanley Cup as a result of the team winning the 2011 Stanley Cup Playoffs.[18] The Bruins did, however, include Cohen in the official Stanley Cup photo, and he was presented with a Stanley Cup ring.[18]

On October 17, 2014, Cohen signed a contract with the Reading Royals of the ECHL.[23] After five scoreless games with the Royals, Cohen was traded to the Missouri Mavericks for future considerations on November 8, 2014.[24][2] When the Mavericks acquired Cohen on November 8, 2014, they put him on their "Suspended" list. On November 10, 2014, the Mavericks activated Cohen from their "Suspended" list and traded him, before he had ever played a game for the team, to the South Carolina Stingrays of the ECHL.[2][25]

Before his season with HC 05 Banská Bystrica was over, Cohen was forced to leave the team due for visa reasons.[28] In light of this, Cohen re-joined with the Nottingham Panthers for the remainder of the 2014-15 season.[28]